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In the two main results, the presence of the sequences related to partitions of sets or numbers, respectively, is evident: labeled topologies create set partitions (induced by
Such a definition is given in section 2 of the present paper; moreover, in Theorem (2.13) we prove that, under some very general conditions on the defining sequence ( a n ), every A ⊆
It transpires that the problem is governed by a rate function which consists of two parts: one contribution comes from the Freidlin-Wentzell theorem whereas a second term reflects
Theorem 1 On the set W of all suitable weak solutions u of equation (1), let µ be a probability measure, invariant for the time-shift, with finite mean dissipation rate.. In a sense,
It was found in ( 4 ) (see Theorem 3.5.2) that for finite moments s ≥ 1 the entropy coding error is related to the asymptotic behavior of the small ball function of the
We apply this LDP to prove that the radius of convergence of the generating function of the collision local time of two independent copies of a symmetric and strongly transient
The proof of Theorem 3 is based on Burkholder’s technique, which reduces the problem of proving a martingale inequality to finding a certain spe- cial function.. The description of
The one in Liggett (1985) and Lindvall (1992) treats only the compact space case, and in Strassen (1965) the result is rather implicit, only briefly mentioned as a special case of
